She was named for George Murray, who served during the late 18th and early 19th centuries.

The turbine developed a total of 15,000 shaft horsepower (11,000 kW) and gave a maximum speed of 27 knots (50 km/h; 31 mph).

[1] The Blackwoods had a range of 4,500 nautical miles (8,300 km; 5,200 mi) at 12 knots (22 km/h; 14 mph).

[3] Murray was laid down by Alexander Stephen and Sons at their Govan shipyard on 30 November 1953, launched on 25 February 1954 and completed on 5 June 1956.

The ship is featured with other Type 14 frigates in the 1960 Norman Wisdom film The Bulldog Breed.